Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1006.0363 · Physical Review E

Universal irreversibility of normal quantum diffusion

Hiroaki S. Yamada, Kensuke S. Ikeda

Published Dec 15, 2010• 10 citations
arXivHTMLPDF

Abstract

Time-reversibility measured by the deviation of perturbed time-reversed motion from the unperturbed motion is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrasting physical nature. Irrespective of the system, there exists a universal minimal quantum threshold above which the system completely loses memory of the past. The time-reversed dynamics as well as the time-reversal characteristics are asymptotically universal curves independent of the details of the systems.

DOI
10.1103/physreve.82.060102

Related papers

Universal Characteristics of Time-irreversibility in Quantum Normal Diffusion(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

Hiroaki S. Yamada, Kensuke S. Ikeda

Time-irreversibility of apparently irreversible phenomena observed in quantum systems with a very small number of degrees of freedom is studied quantitatively by a time-reversal test: the system evolved in the forward-time direction is time-reversed after applying a small perturbation at the reversal time and the separation between the time-reversed perturbed and the time-reversed unperturbed states is measured as a function of perturbation strength. If the system exhibits a normal diffusion, the time-reversal characteristics has a universal threshold of perturbation strength above which a complete loss of memory is realized. A remarkable fact is that, for almost all the model systems we examined, including discrete-time/continuous-time systems and deterministic/stochastic systems, the time reversal characteristics as well as the time-reversal dynamics itself converge asymptotically to universal behaviors independent of the details of the systems, which implies the prototype of quantum irreversibility. Only the diffusive behavior of the critical states in Harper equation deviates significantly from the universal behavior.

物性研究•Dec 5, 2011•0 citations

Time irreversibility of classically chaotic quantum dynamics

Giulio Casati, Boris V. Chirikov

The nature of classically chaotic quantum dynamics is studied by menas of a numerical time reversal experiment. It turns out that there is a fundamental quantum scale below which the system cannot exhibit classical irreversibility to external perturbations. On the other hand, a paradoxical phenomenon manifesting that quantum irreversibility may exceed its classical counterpart is discovered. These features are explained in terms of semicalssical dynamical theory. Introduction Classically chaotic quantum systems in general can exhibit intrinsinc chaotic behaviour on a quite restricted time scale [1], In particular localization phenomena provide direct evidence exhibiting the suppression of quantum ergodicity [2]. On the other hand, recent studies reveal that a many-dimensional system can mimic some aspects peculiar to chaotic dynamics quite well on an unexpectedly long time scale [3]. A remarkable feature that distinguishes chaotic motion from integrable motion is the sensitive dependence of dynamics on external perturbations. For classical dynamical systems such a sensitivity can be well defined by measuring how two nearby trajectories in the phase space separate in time. However, there has been proposed no systematic way to examine the sensitivity of quantum dynamics to external perturbation. In quantum dynamics, it is not possible to trace a well defined trajectory in phase space, because both quantum uncertainty and chaotic instability make a localized wavepacket spread suddenly over the phase space [4]. There is, however, a simple way in which we may test the quantum sensitivity quantitively. This is the time reversal experiment described below. In this chapter I describe several remarkable characteristics of quantal instability which have been clarified by the time reversal experiment.

Cambridge University Press eBooks•Apr 27, 1995•4 citations

Reversibility of dynamics and multiple-quantum coherences

Anatoly K. Khitrin

In spin systems, the decay of the Loschmidt echo in the time-reversal experiment (evolution-perturbation-time-reversed evolution) is linked to the generation of multiple-quantum (MQ) coherences. Unlimited growth of the MQ coherences leads to irreversibility of dynamics. In some cases, one can expect that the deviation of the Loschmidt echo and the second moment of the MQ intensities distribution are linear in time. The criteria of such behavior, called weak irreversibility, are formulated. The proposed approach can be extended beyond spin systems, in order to analyze some general aspects of reversibility of many-body quantum dynamics.

arXiv:1412.8199•Physical Review E•Nov 4, 2015•2 citations

Irreversible dynamics in quantum many-body systems

Markus Schmitt, Stefan K. Kehrein

The concept of irreversibility is necessary to justify the statistical description of many-body systems. Here, the authors study the dynamics of observable echoes in quantum many-body systems occurring when the time-evolution is effectively inverted. For nonintegrable systems they find that small imperfections in the time-reversal procedure that alter the state of the system lead to exponentially decaying echoes. As the corresponding decay rate is largely independent of the strength of the perturbation, an intrinsic sensitivity to the perturbation is revealed. This implies irreversibility of the dynamics for all practical purposes, similar to the situation in chaotic classical systems.

arXiv:1711.00015•Physical review. B./Physical review. B•Nov 9, 2018•24 citations

Generating quantum ensembles via reverse-time quantum diffusions

Maël Bompais, Mădălin Guţă, Juan P. Garrahan

We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schrödinger equation of a forward noising dynamics, we derive the exact reverse-time dynamics for quantum trajectories, whose law coincides with the time-reversal of the original process. We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise but a state-dependent feedback Hamiltonian, a direct analogue of the "score function" of generative classical diffusion models. This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states. We show how the denoising dynamics can be directly learnt from forward trajectory data, and how to exploit purification to initialise the denoising process.

quant-pharXiv:2606.03848•Jun 3, 2026•0 citations

Irreversibility from a Reversible Equation

Hiroshi Ezawa, Koichi Nakamura, Keiji Watanabe

After a discussion on the state of local equilibrium with temperature inhomogeneity, comparing mixture state reprsentation in statistical mechanics and pure state representation in thermo field dynamics, a simple model is solved to show that a reversible equation of motion with the initial condition having inhomogeneous temperature can lead to irreversible, viz. diffusive, behaviour. Yet, the solution is time symmetric exhibiting diffusion both towards future and past.

arXiv:cond-mat/9809208•Sep 15, 1998•0 citations
Time-reversibility measured by the deviation of perturbed time-reversed motion from the unperturbed motion is examined for normal quantum diffusion exhibited by four classes of quantum maps with contrasting physical nature. Irrespective of the system, there exists a universal minimal quantum threshold above which the system completely loses memory of the past. The time-reversed dynamics as well as the time-reversal characteristics are asymptotically universal curves independent of the details of the systems.
Time-irreversibility of apparently irreversible phenomena observed in quantum systems with a very small number of degrees of freedom is studied quantitatively by a time-reversal test: the system evolved in the forward-time direction is time-reversed after applying a small perturbation at the reversal time and the separation between the time-reversed perturbed and the time-reversed unperturbed states is measured as a function of perturbation strength. If the system exhibits a normal diffusion, the time-reversal characteristics has a universal threshold of perturbation strength above which a complete loss of memory is realized. A remarkable fact is that, for almost all the model systems we examined, including discrete-time/continuous-time systems and deterministic/stochastic systems, the time reversal characteristics as well as the time-reversal dynamics itself converge asymptotically to universal behaviors independent of the details of the systems, which implies the prototype of quantum irreversibility. Only the diffusive behavior of the critical states in Harper equation deviates significantly from the universal behavior.
The nature of classically chaotic quantum dynamics is studied by menas of a numerical time reversal experiment. It turns out that there is a fundamental quantum scale below which the system cannot exhibit classical irreversibility to external perturbations. On the other hand, a paradoxical phenomenon manifesting that quantum irreversibility may exceed its classical counterpart is discovered. These features are explained in terms of semicalssical dynamical theory. Introduction Classically chaotic quantum systems in general can exhibit intrinsinc chaotic behaviour on a quite restricted time scale [1], In particular localization phenomena provide direct evidence exhibiting the suppression of quantum ergodicity [2]. On the other hand, recent studies reveal that a many-dimensional system can mimic some aspects peculiar to chaotic dynamics quite well on an unexpectedly long time scale [3]. A remarkable feature that distinguishes chaotic motion from integrable motion is the sensitive dependence of dynamics on external perturbations. For classical dynamical systems such a sensitivity can be well defined by measuring how two nearby trajectories in the phase space separate in time. However, there has been proposed no systematic way to examine the sensitivity of quantum dynamics to external perturbation. In quantum dynamics, it is not possible to trace a well defined trajectory in phase space, because both quantum uncertainty and chaotic instability make a localized wavepacket spread suddenly over the phase space [4]. There is, however, a simple way in which we may test the quantum sensitivity quantitively. This is the time reversal experiment described below. In this chapter I describe several remarkable characteristics of quantal instability which have been clarified by the time reversal experiment.
In spin systems, the decay of the Loschmidt echo in the time-reversal experiment (evolution-perturbation-time-reversed evolution) is linked to the generation of multiple-quantum (MQ) coherences. Unlimited growth of the MQ coherences leads to irreversibility of dynamics. In some cases, one can expect that the deviation of the Loschmidt echo and the second moment of the MQ intensities distribution are linear in time. The criteria of such behavior, called weak irreversibility, are formulated. The proposed approach can be extended beyond spin systems, in order to analyze some general aspects of reversibility of many-body quantum dynamics.
The concept of irreversibility is necessary to justify the statistical description of many-body systems. Here, the authors study the dynamics of observable echoes in quantum many-body systems occurring when the time-evolution is effectively inverted. For nonintegrable systems they find that small imperfections in the time-reversal procedure that alter the state of the system lead to exponentially decaying echoes. As the corresponding decay rate is largely independent of the strength of the perturbation, an intrinsic sensitivity to the perturbation is revealed. This implies irreversibility of the dynamics for all practical purposes, similar to the situation in chaotic classical systems.
We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schrödinger equation of a forward noising dynamics, we derive the exact reverse-time dynamics for quantum trajectories, whose law coincides with the time-reversal of the original process. We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise but a state-dependent feedback Hamiltonian, a direct analogue of the "score function" of generative classical diffusion models. This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states. We show how the denoising dynamics can be directly learnt from forward trajectory data, and how to exploit purification to initialise the denoising process.